# All Questions

98,519 questions
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### Given a set of vertices of the Boolean cube, what is the equivalent union with least number of faces?

For example. Suppose you are compacting binary using the symbol X. Like a pattern that expands to (0,1). Example. BINARY SET 0000 0010 1000 1010 MINIMAL ...
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### Stiefel-Whitney total class with prescribed zeros

First things first, I am aware of the existence of this topic. It's related, but old and my question hasn't been discussed there. So I hope it's not wrong to start a new topic. I'm currently ...
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### Name for mappings that are “not quite projections”

Is there a known name for the following definition? Consider topological spaces $X$, $Y$ and $f: X \rightarrow Y$ a continuous mapping. Then, $f$ is an "almost projection" if there is a topological ...
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### Functoriality of (co)limits in $\infty$-categories

I have some questions about the functoriality of (co)limits in $\infty$-categories, say in the framework of Lurie's Higher Topos Theory. From the general stuff about Kan-extensions (HTT 4.3.2.6) ...
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### Theory of surfaces in $\mathbb{R}^3$ as level sets

Is there a book that treats the classical theory of surfaces in $\mathbb{R}^3$ from the point of view of level sets of a function? I seem to remember someone telling me that such a book exists, but I ...
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### Matching Stochastic Flows

Let $\nu = (\nu_t)_{t \in [0,T]} \in C( [0,T], \mathcal{P}_2(\mathbb{R}) ) ,$ where $\mathcal{P}_2(\mathbb{R})$ denotes the space of probability measures with finite moment equipped with the ...
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### Tiling with incommensurate triangles

Say that two triangles are incommensurate if they do not share an edge length or a vertex angle, and their areas differ. Suppose you'd like to tile the plane with pairwise incommensurate triangles. I ...
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### A problem of four conics

I found a remarkable theorem of four conics as follows some years ago. But it has no proof; I am looking for a proof: Theorem: Take three conics. Suppose that each of them touch a fourth conic at two ...
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### $m-$cycles in $S_n$ modulo an equivalence relation

Let $A$ be the set of all $m-$cycles in $S_n$. Define an equivalence relation $i$ in $A$ by $\sigma_1$ is related to $\sigma_2$ by $i$ if $\sigma_1$ is a power of $\sigma_2$ or viz., then the number ...
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### Are there infinitely many real multiplication fields of abelian surfaces over $\mathbb Q$?

Do there exist infinitely many real quadratic fields $F$ such that there is an abelian surface $A$ over $\mathbb Q$ whose ring of endomorphisms, tensored with $\mathbb Q$, is $F$? Do there exist ...
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### The prime number matrix sieve [on hold]

I have derived the following theorem: An odd positive integer $N=6n−1$ is a prime iff neither of two diophantine equations $6x^2+(6x−1)y=n$ $6x^2+(6x+1)y=n$ has a solution. An odd positive ...
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### Bounds on the L^1 norm of a discrete Fourier spectrum

I am dealing with a function $f$ of the form $$f(t):=\sum_{k=1}^Na_ke^{\mathrm{i}\phi_k t}$$ and I have a promise that 0\leq f(t)\leq C\;\;\;\text{for all}...
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### Relative weight lattice

Let $G$ be a reductive group over an algebraically closed field $k$. Let $T$ be a maximal torus, $B$ be a Borel subgroup and $I_G$ is the set of simple roots. Let $P$ be a parabolic subgroup, $M$ be ...
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### Kato's Euler System for Isogenous Elliptic Curves

Let $E,E^\prime$ be elliptic curves over $\mathbb{Q}$ and also suppose they are $p$-isogenous. How are the Euler systems corresponding to the two isogenous elliptic curves related, if at all?
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### What does the classifying space of a topological monoid classify?

The classifying space $BG$ of a topological group $G$ classifies principal $G$ bundles. I have come to appreciate this. I hope the following question is appropriate for MathOverflow: What does the ...
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### How to understand the sign periodicity of any conditionally convergent series? [on hold]

Given any conditionally convergent series $\sum_{n\geq1} a_n$. I wonder if there is a "standard way/method" to "investigate/estimate" the sign periodicity of $a_n$ by some explicit functions $f(x)$ i....
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### what are the math books worth to read published in 2018? [on hold]

Holidays are approaching fast and books are always great gifts. By math books, I mean undergraduate textbooks, large audience math books, specific field books. The only request is that they have ...
Question: Is there an infinite sequence of primes $\{q_i\}_{i=1}^{\infty}$ that is not too sparse ( $q_n =O(poly(n))$ for a fixed polynomial) for which it is true that for every $k$ there is an $N(k)$ ...
Let $\mathbf{B}$ be an $m\times r$ binary matrix taking values in $\{0,1\}$, and assume that $m\geq r$. I am wondering what can be said about the recovery of $\mathbf{B}$ from $\mathbf{B}\mathbf{B}^T$....